//https://leetcode.cn/problems/unique-paths-iii/

class Solution {
    int dx[4] = { 0,0,1,-1 };
    int dy[4] = { 1,-1,0,0 };
    bool vist[21][21];
    int ret, step;
    int m, n;
public:
    int uniquePathsIII(vector<vector<int>>& grid)
    {
        m = grid.size();
        n = grid[0].size();
        int bx, by;
        for (int i = 0; i < m; i++)
        {
            for (int j = 0; j < n; j++)
            {
                if (grid[i][j] == 0) step++;
                else if (grid[i][j] == 1)
                {
                    bx = i;
                    by = j;
                }
            }
        }
        step += 2;
        vist[bx][by] = true;
        dfs(grid, bx, by, 1);

        return ret;

    }

    void dfs(vector<vector<int>>& grid, int i, int j, int count)
    {
        if (grid[i][j] == 2)
        {
            if (count == step)
                ret++;

            return;
        }

        for (int k = 0; k < 4; k++)
        {
            int x = i + dx[k];
            int y = j + dy[k];
            if (x >= 0 && x < m && y >= 0 && y < n && !vist[x][y] && grid[x][y] != -1)
            {
                vist[x][y] = true;
                dfs(grid, x, y, count + 1);
                vist[x][y] = false;
            }
        }
    }
};